I'd be curious to see your setup, purely because I have never found a way to have the iGPU handle the HDMI output. It seems it's directly soldered to the Nvidia card.
Strange. I thought that solution (output soldered onto the GeForce) was discontinued a long time ago for this range of machines. My setup works really well both with the HDMI output, with the Thunderbolt output, and of course with the laptop display.
I have this going on two very similar machines: A circa 2017 XPS 9560, and a circa 2020 XPS 7590. Both are 15". I don't have the 9560 near me at the moment, but the 7590 has
01:00.0 3D controller: NVIDIA Corporation TU117M [GeForce GTX 1650 Mobile / Max-Q] (rev ff)
I'm happy to help you debug if you want. What happens if you remove all nvidia drivers and plug something into the HDMI port? Do you notice any response from the external screen if you hit for example control f2?
